Exploring Addition and Subtraction Situations Math Alliance Originally from: March 8 & 9, 2010

Thinking About Addition and Subtraction The most familiar way to think of addition and subtraction are as combining and taking away. (Beckmann, 2005)

Word Problem Structures What were they? Add to (Join) Part-Part-Whole (Put Together/Take Apart) Take Away (Take From, Separate) Compare

Representing Word Problem Structures 3 6 ? 9 ? 3 One set of objects being combined or separated. Two sets of objects being compared.

Match Diagrams to Word Problem Structures Take turns completing the activity. Pick a diagram. Study it quietly on your own. Decide on which story it matches. Describe why you think the diagram matches that particular word problem.

Add to or Join Clare had 3 bears. After she got some more bears, Clare had 9 bears. How many bears did Clare get? 3 + ? = 9 Clare had some bears. After she got 3 more bears from a friend, Clare had 9 bears. How many bears did Clare have to begin with? ? + 3 = 9

Take Away or Separate 9 – ? = 3 ? – 3 = 6 Clare had 9 bears. After she gave away some bears to her brother, Clare still had 3 bears. How many bears did Clare give away? 9 – ? = 3 Clare had some bears. After she gave away 3 bears to her cousin, she had 6 bears left. How many bears did Clare have to begin with? ? – 3 = 6

Part-Part-Whole Two distinct parts that make a whole; no action. Clare has some red bears and some blue bears. She has 3 blue bears. All together, Clare has 9 bears, and all of them are either red or blue. How many red bears does Clare have? ? + 3 = 9 Clare has some red bears and some blue bears. She has 3 red bears and she has 6 blue bears. How many bears does Clare have? 3 + 6 = ?

Compare Problems A comparison of two quantities or sets. Clare has 3 red bears. She also has 6 more blue bears than red bears. How many blue bears does Clare have? 3+6 = ? Clare has 9 red bears and 3 blue bears. How many more red bears does Clare have than blue bears? 3 + ? = 9 or 9 - 3 = ?

Debrief Which of these problems do you think might be hardest for young children? Why?

Basic Addition & Subtraction Equations A + B = C C = A + B Subtraction D – E = F F = D – E In what way does this become problematic when one term is missing?

Addition and Subtraction Relationships The relationship between addition and subtraction gives rise to problems that can be solved by addition but are not “add to” and problems that can be solved by subtraction, but are not “take away”. (Beckmann, 2005)

Thinking About Solution Approaches 6 + 3 = ? – 6 = 9 Can be solved by adding 6 + ? = 9 ? + 6 = 9 9 – 6 = ? 9 – ? = 6 Can be solved by subtracting